Since the pioneering work by Fradkin and Tseytlin [1]}, there has been much interest in conformal higher-spin (CHS) theories in diverse dimensions, see
[2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}
for an incomplete list of works published within a quarter-century after [1]}.
This interest has truly exploded in the last decade (see, e.g., [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]} and references therein), and some comments
on the literature will be given below. In the case of three dimensions, higher-spin generalisations of the Cotton tensor are of central importance and lie at the heart of many recent studies [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}, [36]}, [37]}, [38]}.
Linearised higher-spin Cotton tensors in AdS\(_3\)  will be the main object of interest in this work.
